Final answer:
To find the cosine of angle B, we can use the law of cosines by substituting the given values into the formula. By simplifying and solving for cos(B), we find that it is approximately -0.8594.
Step-by-step explanation:
To find the cosine of angle B, we need to use the law of cosines. The law of cosines states that c^2 = a^2 + b^2 - 2ab *cos(C), where c is the side opposite angle C. In this case, angle B is opposite side X, so we can substitute the given values into the formula:
X^2 = Y^2 + Z^2 - 2YZ*cos(B)
Substituting the given values, we have:
(18 inches)^2 = (80 inches)^2 + (82 inches)^2 - 2(80 inches)(82 inches)*cos(B)
Simplifying and solving for cos(B), we get:
cos(B) = (18 inches)^2 - (80 inches)^2 - (82 inches)^2 / - 2(80 inches)(82 inches)
cos(B) = -0.8594